Methods for computing a real-time step length and speed of a running or walking individual

ABSTRACT

A method for calculating an estimation of the speed {circumflex over (V)}[n′] of an individual walking along a path, over a time window including: computing a step length  [n′] of the individual, calculating the speed {circumflex over (V)}[n′] using the following formula: 
         {circumflex over (V)} [ n ′]= [ n ′]× [ n ′].

FIELD OF THE INVENTION

The invention relates to methods for computing a real-time estimation ofthe step length and the speed of a walking or running individual.

BACKGROUND OF THE INVENTION

Gait speed and step length are important parameters to characterize anindividual's daily activities. In sport applications for instance, speedmay be used to evaluate athletes and to design personalized trainingsessions, with a view to improve performance and decrease the risk ofinjury. In clinical applications, speed is used to evaluate theindividual's health, thereby helping doctors diagnose, predict andprevent many diseases such as diabetes, overweight or cardiovascularpathologies.

Global Navigation Satellite System (GNSS) is a basic system widely usedto measure an individual's gait speed. GNSS is accurate, and manywearable devices have been designed to embed a GNSS transponder, themeasurements of which may be used to compute the individual's gait speedeven in real-life conditions. However, there are locations where theGNSS signal is weak or might even be lost due to the lack of satellitecoverage, such as indoors, tunnels, near high buildings, narrow valleys.In addition, a GNSS transponder is very power consuming, whereby it ispreferable to use it sporadically instead of continuously.

Inertial sensors-based systems are yet another way to measure anindividual's gait speed in daily life. While most inertial sensors areused attached to lower limb of the individual's body (such as feet,shanks, thighs), few are used attached to upper limbs (such as trunk andwaist).

It is also known to use multiple sensors attached to different parts ofthe individual's body, the measurements of which are combined to enhanceperformance of gait speed estimation.

Inertial sensors-based systems estimate gait speed through multiplyinggait cadence (i.e. the number of steps per time unit) by step length.Those systems usually compute the cadence by sensing certain moments(e.g. hill-strike, toe-off, mid-swing) during the different gait phases.

In usual inertial sensors-based systems, a step length is computedthrough geometric modelling of the individual's gait (e.g. based oninverse pendulum movement), double integration of acceleration, or anabstract modelling of the gait based on machine learning.

One main advantage of the inertial-based systems is their possible usagein daily life conditions. Another advantage of the inertial systems istheir acceptable accuracy. One main drawback, however, is that thosesystems need sensor calibration at the beginning of each measurementphase, which requires expertise from the user to wear them on the body.Another drawback is that the location of the sensors on the user's bodyare often regarded as an inconvenient, especially when a plurality ofsensors are required. This might explain their commercial failure.

Only recently were methods introduced to estimate the gait speed of anindividual based on wrist-worn inertial sensors.

Most known methods use an abstract modelling, which extracts severalfeatures from raw data and then build a regression model to estimatespeed. Basic features for the wrist-based speed estimation are energy ofthe signal, cadence, mean crossing rate, and statistical features likemean, standard deviation, mode, and median of acceleration signal, seee.g. B. Fasel et al., “A wrist sensor and algorithm to determineinstantaneous walking cadence and speed in daily life walking,” Med.Biol. Eng. Comput., vol. 55, pp. 1773-1785, 2017. Fasel also proposesintensity of the movement as a feature, which is a multiplication ofmean and standard deviation of the wrist acceleration. Fasel yet alsoproposed the slope of the path (based on pressure sensor) as a featurefor speed estimation.

However, even the best methods (including Fasel's) only exploit a littlepiece of useful information from the physics of hand and body movements.Moreover, the existing methods rely upon a general speed model, whichresults from an effort to standardize the individual to an average of alarge population of humans. While efforts were made to somewhat adaptthe general speed model with age, sex, height, and weight parameters,the model remains a standard ignorant of the strategy that eachindividual might exploit to manage his/her gait speed during physicaleffort.

SUMMARY OF THE INVENTION

It is an object of the present invention to propose a method foraccurate and real-time estimation of the step length of a walking orrunning individual.

Another object of the invention is to propose a personalized methodcapable of learning the individual's gait and automatically adapt tohis/her activity behaviour.

Another object of the invention is to propose a method that might beimplemented within a wrist-wearable device, providing easy-to-usemeasurements for long-term monitoring of physical activities.

Another object of the invention is to propose a low-consumptioncomputing method to increase autonomy of the wrist-wearable device.

It is therefore proposed, in a first aspect a method for computing anestimation of the step length of an individual over a time window,according to claim 1.

It is proposed, in a second aspect, a method for calculating anestimation of the speed of the individual over the time window,according to claim 10.

It is proposed, in a third aspect, a computer program productimplemented on a readable memory connected to a calculation unit, saidcomputer program including the instructions for conducting the methodfor computing the step length and/or the method for computing the speedas disclosed hereinbefore.

It is proposed, in a fourth aspect, a wrist-wearable device including acalculation unit and a readable memory connected to the readable memory,said readable memory being implemented with the computer programmentioned here above.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and further objects and advantages of the invention willbecome apparent from the detailed description of preferred embodiments,considered in conjunction with the accompanying drawings.

FIG. 1 is a perspective view of an individual having a wrist-wearabledevice attached to the wrist.

FIG. 2 is a schematic perspective view of a path followed by anindividual during a walking (or running) session.

FIG. 3, FIG. 4 and FIG. 5 are schematic side views of an individualrunning on a path with no slope (FIG. 3), positive slope (FIG. 4) andnegative slope (FIG. 4).

FIG. 6 is a wrist-wearable device embedding a system for computing areal-time estimation of the step length and speed of a walking orrunning individual.

FIG. 7 is a perspective view showing an individual's hand in movement,with the wrist-wearable device of FIG. 6 attached to it.

FIG. 8 is a diagram summarizing different phases and steps of a methodfor computing a real-time estimation of the step length and speed of awalking or running individual.

FIG. 9 is a diagram showing two pairs of superposed curves: on the left,a pair of superposed speed curves of a running individual, including aGNSS-built reference curve, and a prediction curve computed with themethod of the invention; on the right, the same for a walkingindividual.

DETAILED DESCRIPTION

On FIG. 1 is schematically drawn an individual on foot 1. The individual1 is supposed to be healthy and have all his/her members, including legsand arms, the arms having wrists 2. The individual 1 defines a verticalsagittal plane P1 (which is the global symmetry plane of the individual1) and a vertical front plane P2, which is perpendicular to the sagittalplane P1. As depicted on FIG. 1, a wrist-wearable device or “smartwatch”3 is attached to at least one of the individual's wrists, here to theright wrist 2.

The smartwatch 3 is configured to monitor activity and infer variousparameters of the individual 1 while he/she is moving on foot (i.e.either running or walking) on a path 4, the variations of altitude ofwhich are voluntarily exaggerated on FIG. 2.

Indeed, while some portions of the path 4 may be flat (as shown on FIG.3), other portions may be inclined and have a slope A which, from theindividual's point of view, may be positive (FIG. 4) or negative (FIG.5).

The individual 1 is moving:

-   -   at a gait speed noted V (expressed in m·s⁻¹),    -   at a cadence noted cad (expressed in s⁻¹ or Hz),    -   with a step length noted SL (expressed in m).

The smartwatch 3 is equipped with:

-   -   a calculation unit 5,    -   a readable memory 6 connected to the calculation unit 5,    -   an accelerometer 7, a barometer 8 and a GNSS transponder 9 all        connected to the calculation unit 5.

The calculation unit 5, readable memory 6, accelerometer 7, barometer 8and GNSS transponder 9 are embedded in a casing 10 attached to the wrist2 by means of a strap or bracelet 11.

The readable memory 6 is implemented with a computer program includinginstructions for conducting a method for computing at least anestimation of the step length over a time window n, noted

[an], of the individual 1 along the path 4, and preferably also anestimation of his/her gait speed over time window n, noted {circumflexover (V)}[n].

The computed step length

[n] and computed speed {circumflex over (V)}[n] are linked to oneanother by the following equation:

{circumflex over (V)}[n]=

[n]×

[n],

where

[n] is an estimated cadence of the individual 1 over time window n.

It should be noted that n is an integer where n ∈ [1, . . . N], N beingan integer higher than 1. [1, . . . N] represents a time range startingfrom a first time window n=1 corresponding to the beginning of thecomputing to a last time window n=N corresponding to the end of thecomputing. In a preferred embodiment, time windows are 7-second longwith 6-second overlap.

The method uses instant acceleration measures provided by theaccelerometer 7 and instant atmospheric pressure measures provided bythe barometer 8.

The accelerometer 7 is configured to deliver acceleration measures alongthree perpendicular axes, namely:

-   -   a first acceleration along an X axis perpendicular to the arm of        the individual 1 and parallel to his/her sagittal plane P1,    -   a second acceleration along a Y axis parallel to the arm of the        individual 1 and parallel to his/her sagittal plane P1,    -   a third acceleration along a Z axis perpendicular to the arm of        the individual 1 and parallel to his/her front plane P2.

For each axis X, Y, Z, z acceleration samples are taken per window, zbeing an integer higher than 1:

-   -   S_(x) ^(i)[n] is the i-th acceleration sample along the X axis,        delivered by the accelerometer (7) along time window n,    -   S_(y) ^(i)[n] is the i-th acceleration sample along the Y axis,        delivered by the accelerometer (7) along time window n,    -   S_(z) ^(i)[n] is the i-th acceleration sample along the Z axis,        delivered by the accelerometer (7) along time window n.

For convenience, in the rest of the description, the following notationswill be used:

S _(x)=(S _(x) ^(i))_(i∈[1, . . . z])

S _(y)=(S _(y) ^(i))_(i∈[1, . . . z])

S _(z)=(S _(z) ^(i))_(i∈[1, . . . z])

Likewise, the barometer 8 is configured to deliver z atmosphericpressure samples per window:

-   -   P^(i)[n] is the i-th pressure sample delivered by the barometer        (8) within time window n,    -   P[n] is the average pressure within time window n.

For convenience, in the rest of the description, the following notationwill be used: P=(P^(i))_(i∈[1, . . . z]).

The proposed method relies on a machine learning approach based upon thehypothesis that the step length

may be computed using a function, denoted g, of a set of M gait featuresF₁, F₂, . . . , F_(M) (M being an integer):

=g(F ₁ , F ₂ , . . . , F _(m)).

Six gait features (M=6) are considered here, five of which are computedfrom the acceleration measures S_(x), S_(y), S_(z) delivered by theaccelerometer 7, and one of which is computed from the atmosphericpressure measures P delivered by the barometer 8.

F₁[n] is an estimated gait cadence of the individual over time window n:F₁[n]=

[n]. In one preferred embodiment, feature F₁[n]=

[n] is estimated from a known algorithm proposed by Fasel (op. cit. pp.1775-1778). More precisely, feature F₁[n] over time window n is computedby the steps of:

-   -   computing the norms of the acceleration measures (S_(x)[n],        S_(y)[n], S_(z)[n])=(S_(x) ^(i)[n], S_(y) ^(i)[n], S_(z)        ^(i)[n])_(i∈[1, . . . z]) delivered by the accelerometer 7,    -   applying a Fast Fourier Transform to such computed acceleration        norm,    -   applying a Comb filter to such Fast Fourier Transform, resulting        in a cadence likelihood function,    -   attributing the maximum value of the likelihood function in the        range of frequencies below 2 Hz to F₁[n]=        [n].

F₂[n] is an estimated slope A of the path 4. It is assumed that the steplength SL decreases uphill (where slope A is positive, FIG. 4) andincreases downhill (where slope A is negative, FIG. 5). In one preferredembodiment, feature F₂[n] over time window n is computed from theatmospheric pressure measures P[n] delivered by the barometer 8. Moreprecisely, a line is fitted to −P[n] using a least square method, andthe slope of this line is extracted as the slope of feature F₂[n]. Inother words, F₂[n]=A≡−P[n] where the symbol ≡ represents correspondencebetween A and the linear coefficient of the regression line fitting thevariations of −P[n]. This is reflected by the following equation:

${{F_{2}\lbrack n\rbrack} = {- \frac{\sum\limits_{i = 1}^{z}{\left( {i - \overset{\_}{\iota}} \right)\left( {{P^{i}\lbrack n\rbrack} - {\overset{\_}{P}\lbrack n\rbrack}} \right)}}{\sum\limits_{i = 1}^{z}\left( {i - \overset{\_}{\iota}} \right)^{2}}}},$

where l is computed as follows:

$\overset{\_}{\iota} = {\frac{1}{z}{\sum\limits_{i = 1}^{z}{i.}}}$

F₃[n] is an estimated energy of the acceleration measures S_(y) alongthe Y axis, over time window n. It is assumed there is a neural couplingbetween the arms and feet movements during gait. Indeed, when theindividual increases his step length, the range of arm movement isincreased, which leads to an increase in the energy of the accelerationmeasures S_(y) along the Y axis (the one aligned with the wrist). In onepreferred embodiment, feature F₃[n] is computed as the standarddeviation of acceleration S_(y) over time window n:

F ₃[n]=std(S _(y)[n]), that is to say

F ₃[n]=std(S _(y) ^(i)[n])_(i∈[1, . . . z]).

F₄[n] is an estimated mean absolute jerk of wrist acceleration over timewindow n. During gait periods, especially running, regular impacts arewitnessed on the wrist 2 from variations of accelerations, the frequencyof which is equal to the step frequency. The mean absolute value of jerk(i.e. the differential of acceleration) provides information about theenergy of such impacts. In one preferred embodiment, feature F₄[n] iscomputed as the mean of the differential of the acceleration measuresS_(y) along the Y axis:

F ₄[n]=mean(|S _(y) ^(i)[n]−S _(y) ^(i−1)[n]|)_(i∈[1, . . . z]).

F₅[n] is an estimated energy of wrist swing over time window n. It is anestimation of energy of the acceleration measures S_(x) along X axis andS_(z) along Z axis. When the step length is increased during walking,the wrist swing increases, thereby increasing its energy. Feature F₅[n]of wrist swing is computed through the following equation, whichprovides the standard deviation of acceleration norm of S_(x) along theX axis and S_(z) along the Z axis:

F ₅[n]=std(√{square root over (S _(x)[n]² +S _(z)[n]²)}), that is to say

F ₅[n]=std(√{square root over (S _(x) ^(i)[n]² +S _(z)^(i)[n]²)})_(i∈[1, . . . z]).

F₆[n] is an estimated mean of acceleration norm over time window n.During walking, the wrist 2 oscillates around the trunk while the bodyis moving forward. Feature F₆[n], which denotes a degree of the bodymovement, is computed as follows:

F ₆[n]=mean(√{square root over (S _(x)[n]² +S _(y)[n]² +S _(z)[n]²)}),that is to say

F ₆[n]=mean(√{square root over (S _(x) ^(i)[n]² +S _(y) ^(i)[n]² +S _(z)^(i)[n]²)})_(i∈[1, . . . z]).

The fact that the natures of the movement of wrist 2 during walking andrunning are different has been taken into consideration. For instant,during walking, the wrist 2 follows a pendulum swing movement that isabsent in running.

In order to better fit the model to the type of gait, differentcombinations of features F₁, F₂, . . . , F₆ are used to implement themethod in running and walking, respectively.

More precisely, while F₁, F₂, F₃, F₄ are used for computing function gin a running situation, F₁, F₂, F₄, F₅, F₆ are used for computing saidfunction in a walking situation.

The method for computing the step length

includes two procedures, namely:

-   -   a personalization procedure, including:        -   an offline training phase 100 based upon GNSS data and that            is conducted only once at the beginning of the path 4, and        -   an online training phase 200 which is initiated through the            results provided by the offline training phase and which is            repeated along the path 4,    -   an estimation procedure 300.

Personalisation Procedure

Under the personalisation procedure, the GNSS transponder 9 is ON anddelivers instant speeds of the smartwatch 3.

The offline training phase 100 is conducted over an initial time window0 that does not represent the beginning of the running or walkingsession but a few seconds later. The offline training phase 100 aims atbuilding an initial model to estimate the step length and the speed ofthe individual, and includes the steps of:

i) Measuring 102 an initial speed V[0] by the GNSS transponder 9 overthe initial time window 0.

ii) Computing 104 an initial step cadence

[0] from acceleration measures S_(x)[0], S_(y)[0], S_(z)[0] delivered bythe accelerometer 7 over the initial time window 0.

Initial step cadence

[0] is computed using the steps to compute feature F₁[n], wherein n=0 (

[0]=F₁[0]).

iii) Computing 106 an initial step length SL[0] from the initial speedV[0] and the initial step cadence

[0].

The initial step length SL[0] is inferred from the initial speed V[0]and the initial step cadence

[0] according to the following equation:

${{SL}\lbrack 0\rbrack} = {\frac{V\lbrack 0\rbrack}{\lbrack 0\rbrack}.}$

iv) Computing 108 an initial vector of features X[0] from theacceleration measures S_(x)[0], S_(y)[0], S_(z)[0] and the atmosphericpressure P[0] over the initial time window 0.

The initial vector of features X[0] is computed as follows:

For running:

X[0]=[1 F ₁[0] F ₂[0] F ₃[0] F ₄[0] F ₂ ²[0]],

For walking:

X[0]=[1 F ₁[0] F ₂[0] F ₄[0] F ₅[0] F ₆[0]].

F₁[0], F₂[0], F₃[0], F₄[0], F₅[0] and F₆[0] are computed using the stepsto compute F₁[n], F₂[n], F₃[n], F₄[n], F₅[n] and F₆[n], wherein n=0.

v) Computing 110 an initial coefficient vector β[0] from the initialvector of features X[0] and the initial step length S L[0], following aleast square method.

The initial coefficient vector β[0] is computed from the initial vectorof features X[0] and the initial step length SL[0]:

β[0]=(X[0]^(T) X[0])⁻¹ X[0]^(T) SL[0],

where (X[0]^(T)X[0])⁻¹ is called initial dispersion matrix and is alsonoted D[0] in a simplified notation.

The previous equation may therefore be written as follows:

β[0]=D[0]X[0]^(T) SL[0].

β[0], X[0], D[0], SL[0], V[0] and

[0] are referred to as initial parameters.

The online training phase 200 is performed once the offline trainingphase 100 is over. The online training phase 200 aims at personalizingthe initial model built during the offline training phase 100, andcomprises the following steps, sporadically repeated for several timewindows n:

i) Measuring 202 an instant speed V[n] by the GNSS transponder 9 overtime window n.

ii) Computing 204 an instant cadence

[n] from the acceleration measures S_(x)[n], S_(y)[n], S_(z)[n]delivered by the accelerometer 7 over time window n.

The instant step cadence

[n] is computed using the steps to compute feature F₁. As a reminder,F₁[n]=

[n].

iii) Computing 206 an instant step length SL[n] from the instant speedV[n] and the instant step cadence

[n]

${{SL}\lbrack n\rbrack} = \frac{V\lbrack n\rbrack}{\lbrack n\rbrack}$

iv) Computing 208 an instant vector of features X[n] from theacceleration measures S_(x)[n], S_(y)[n], S_(z)[n] delivered by theaccelerometer 7 and atmospheric pressure measures P[n] delivered by thebarometer 8 over time window n.

The instant vector of feature X[n] is computed as follows:

For running:

X[n]=[1 F ₁[n] F ₂[n] F ₃[n] F ₄[n] F ₂[n]²],

For walking:

X[n]=[1 F ₁[n] F ₂[n] F ₄[n] F ₅[n] F ₆[n]].

v) Computing 210 an instant coefficient vector β[n] from the precedingcoefficient vector β[n-1] following a recursive least square method.

The instant coefficient vector [n] is computed as follows:

β[n]=β[n-1]+D[n]X[n](SL[n]−X[n]^(T)β[n-1]),

where D[n] is a dispersion matrix defined (in theory) byD[n]=(X[n]^(T)X[n])⁻¹. However, to simplify calculation and hence limitmemory space, the dispersion matrix D[n] is computed according to thefollowing recursive equation:

D[n]=D[n-1](I−X[n](I+X[n]^(T) D[n-1]X[n])⁻¹ X[n]^(T) D[n-1]),

where I denotes the identity matrix.

The recursive computing of equation for computing β[n] starts from β[1]:

β[1]=β[0]+D[1]X[1] (SL[1]−X[1]^(T)β[0]),

where D[1] is computed using equation for computing D[n] in which theinitial dispersion matrix D[0]=(X[0]^(T)X[0])⁻¹ is injected:

D[1]=D[0](I−X[1](I+X[1]^(T) D[0]X[1])⁻¹ X[1]^(T) D[0]).

Estimation Procedure

Under the estimation procedure 300, the GNSS transponder 9 is OFF. Theestimation procedure aims at estimating the speed, cadence and steplength of the individual using only the inertial sensors.

The estimation procedure 300 includes the following steps, for anarbitrary time window n′, n′ ∈ [1, . . . , N]:

i) Computing 302 an instant vector of features X[n′] from theacceleration measures S_(x)[n′], S_(y)[n′], S_(z)[n′] delivered by theaccelerometer 7 and atmospheric pressure measures P[n′] delivered by thebarometer 8 over time window n′.

ii) Computing 304 an instant step length

[n′] from the instant vector of features X[n′] and the most updatedcoefficient vector β[n], using the following formula:

[n′]=X[n′]β[n].

iii) Computing 306 an instant cadence

[n′] from the acceleration measures S_(x)[n′], S_(y)[n′], S_(z)[n′]delivered by the accelerometer 7 over time window n′.

iv) Computing 308 an instant speed {circumflex over (V)}[n′] from theinstant step length

[n′] and the instant cadence

[n′], using the following formula:

{circumflex over (V)}[n]=

[n′]×

[n′].

This method provides an acceptable memory consumption cost and iscapable of providing real-time computing of the step length

[n′] and the speed {circumflex over (V)}[n′] over a time window n′. Theuse of the disclosed recursive least square method for computing thecoefficient vectors provides good results without the need of allprevious computed data.

Indeed, the method was tested on thirty healthy active volunteers whoparticipated to a 90 minutes outdoor walking and running on a pathhaving various terrain conditions including flat, uphill and downhill.

FIG. 9 shows that the computed speed (in bold line) is close to theactual one (measured through a GNSS, in thin line), whichever the gait(running, on the left; walking, on the right).

This method is inherently user-dependent and hence personalized to eachindividual. It provides an online learning process where the step lengthand speed are inferred from instant inputs and from previouscomputations using a recursive least square model.

The tests conducted on volunteers showed that the error graduallydecreases along the path. It proves to have low power consumption, highaccuracy, practicality (the method is implemented in a wrist-wearabledevice) and good ergonomics (no need to calibrate sensors). This methodis suitable for a daily use on a long-term basis.

1-12. (canceled)
 13. A method for computing an estimation of the steplength

[n′] of an individual running along a path, over a time window n′, n′being an integer higher than or equal to 1, said individual beingequipped with a wrist-wearable device comprising: a calculation unit, aGNSS transponder configured to deliver instant speeds of the device, abarometer configured to deliver instant atmospheric pressure measures(P), an accelerometer configured to deliver instant accelerationmeasures along three perpendicular axes, namely: a first accelerationS_(x) along an X axis perpendicular to the wrist and parallel to asagittal plane (P1) of the individual; a second acceleration S_(y) alonga Y axis parallel to the wrist and parallel to the sagittal plane (P1)of the individual; a third acceleration S_(z) along a Z axisperpendicular to the wrist and parallel to a front plane (P2) of theindividual; said method comprising the following steps, carried out bythe calculation unit: computing a vector of features X[n] over a timewindow n, n being an integer higher than or equal to 1, as follows:X[n]=[1 F ₁[n] F ₂[n] F ₃[n] F ₄[n] F ₂ ²[n]] where: feature F₁[n] is aninstant cadence

[n] of the individual over time window n, computed from the norms of theinstant acceleration measures S_(x)[n],S_(y)[n],S_(z)[n] delivered bythe accelerometer over time window n, feature F₂[n] is an instant slopeof the path computed from the instant atmospheric pressure measures(P[n]) delivered by the barometer over time window n, feature F₃[n] isan instant energy of the second acceleration measures S_(y)[n] deliveredby the accelerometer over time window n, feature F₄[n] is an instantmean absolute jerk of the second acceleration measures S_(y)[n]delivered by the accelerometer over time window n, computing acoefficient vector β[n] over time window n as follows:β[n]=β[n-1]+D[n]X[n] (SL[n]−X[n]^(T)β[n-1]) where: D[n] is thedispersion matrix of the instant vector of features X[n],${{{SL}\lbrack n\rbrack} = \frac{V\lbrack n\rbrack}{\lbrack n\rbrack}},$V[n] is a speed of the wrist-wearable device, measured by the GNSStransponder over time window n, β[0] is an initial parameter, computinga vector of features X[n′] over time window n′, as follows:X[n]′=[1 F ₁[n′] F ₂[n′] F ₃[n′] F ₄[n′] F ₂ ²[n′]] computing the steplength

[n′] as follows:

[n′]=X[n′]β[n]
 14. A method for computing an estimation of the steplength

[n′] of an individual walking along a path, over a time window n′, n′being an integer higher than or equal to 1, said individual beingequipped with a wrist-wearable device comprising: a calculation unit, aGNSS transponder configured to deliver instant speeds of the device, abarometer configured to deliver instant atmospheric pressure measures(P), an accelerometer configured to deliver instant accelerationmeasures along three perpendicular axes, namely: a first accelerationS_(x) along an X axis perpendicular to the wrist and parallel to asagittal plane (P1) of the individual; a second acceleration S_(y) alonga Y axis parallel to the wrist and parallel to the sagittal plane (P1)of the individual; a third acceleration S_(z) along a Z axisperpendicular to the wrist and parallel to a front plane (P2) of theindividual; said method comprising the following steps, carried out bythe calculation unit: computing a vector of features X[n] over a timewindow n, n being an integer higher than or equal to 1 as follows:X[n]=[1 F ₁[n] F ₂[n] F ₄[n] F ₅[n] F ₆[n]] where: feature F₁[n] is aninstant cadence

[n] of the individual over time window n, computed from the norms of theinstant acceleration measures S_(x)[n],S_(y)[n],S_(z)[n] delivered bythe accelerometer over time window n, feature F₂[n] is an instant slopeof the path computed from the instant atmospheric pressure measures(P[n]) delivered by the barometer over time window n, feature F₃[n] isan instant energy of the second acceleration measures S_(y)[n] deliveredby the accelerometer over time window n, feature F₄[n] is an instantmean absolute jerk of the second acceleration measures S_(y)[n]delivered by the accelerometer over time window n, computing acoefficient vector β[n] over time window n as follows:β[n]=β[n-1]+D[n]X[n] (SL[n]−X[n]^(T)β[n-1]) where: D[n] is thedispersion matrix of the instant vector of features X[n],${{{SL}\lbrack n\rbrack} = \frac{V\lbrack n\rbrack}{\lbrack n\rbrack}},$V[n] is a speed of the wrist-wearable device, measured by the GNSStransponder over time window n, β[0] is an initial parameter, computinga vector of features X[n′] over time window n′, as follows:X[n′]=[1 F ₁[n′] F ₂[n′] F ₃[n′] F ₄[n′] F ₂ ²[n′]] computing the steplength

[n′] as follows:

[n′]=X[n′]β[n].
 15. The method according to claim 13, wherein featureF₁[n] is computed by the steps of: computing the norms of theacceleration measures (S_(x) ^(i)[n] S_(y) ^(i)[n] S_(z)^(i)[n])_(i ∈ [1, . . . z] delivered by the accelerometer,) applying aFast Fourier Transform to such computed acceleration norm, applying aComb filter to such Fast Fourier Transform, resulting in a cadencelikelihood function, attributing the maximum value of the likelihoodfunction in the range of frequencies below 2 Hz to F₁[n].
 16. The methodaccording to claim 13, wherein feature F₂[n] is computed as follows:${{F_{2}\lbrack n\rbrack} = {- \frac{\sum\limits_{i = 1}^{z}{\left( {i - \overset{\_}{i}} \right)\left( {{P^{i}\lbrack n\rbrack} - {\overset{\_}{P}\lbrack n\rbrack}} \right)}}{\sum\limits_{i = 1}^{z}\left( {i - \overset{\_}{i}} \right)^{2}}}},$where: P^(i)[n] is the i-th pressure sample delivered by the barometerwithin time window k, P[n] is the average pressure within time window n,ī is computed as follows:$\overset{\_}{i} = {\frac{1}{z}{\sum\limits_{i = 1}^{z}i}}$ where z isnumber of samples within time window n.
 17. The method according toclaim 13, wherein feature F₃[k] is computed as the standard deviation ofsecond acceleration measures S_(y)[n]:F ₃[n]=std(S _(y)[n]).
 18. The method according to claim 13, whereinfeature F₄[n] is computed as follows:F ₄[n]=mean(|S _(y) ^(i)[n]−S _(y) ^(i−1)[n]|) where S_(y) ^(i)[n] isthe i-th acceleration sample along the Y axis, delivered by theaccelerometer (7) within time window n.
 19. The method according toclaim 14, wherein feature F₅[n] is computed as follows:F ₅[n]=std(√{square root over (S _(x) ²[n]+S _(z) ²[n])}).
 20. Themethod according to claim 14, wherein the instant mean F₆[n] ofacceleration norm is computed as follows:F ₆[n]=mean(√{square root over (S _(x) ²[n]+S _(y) ²[n]+S _(z) ²[n])})21. The method according to claim 13, wherein D[n] is computed asfollows:D[n]=D[n-1](I−X[n](I+X[n]^(T) D[n-1]X[n])⁻¹ X[n]^(T) D[n-1]), whereD[0]=(X[0]^(T) X[0])⁻¹, X[0] is an initial parameter.
 22. The method forcalculating an estimation of the speed {circumflex over (V)}[n′] of anindividual walking along a path, over a time window n′, comprising:computing the step length

[n′] of the individual according to the method of claim 13, calculatingthe speed {circumflex over (V)}[n′] using the following formula:{circumflex over (V)}[n′]=

[n′]×

[n′].
 23. A computer program product implemented on a readable memoryconnected to a calculation unit, said computer program comprisinginstructions for conducting a method according to claim
 13. 24. Awrist-wearable device comprising a calculation unit and a readablememory connected to the readable memory, said readable memory beingimplemented with the computer program according to claim 23.